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17.40 (2010)

Solved

Let $N$ be a nilpotent subgroup of a finite group $G$. Do there always exist elements $x, y \in G$ such that $N \cap N^x \cap N^y \leqslant F(G)$?

Contributor: E. P. Vdovin

Progress

Yes, such elements always exist, mod CFSG (V. I. Zenkov, Siberian Math. J., 62, no. 4 (2021), 621–637).

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